That’s a nice video! Is there a reference for Ochiai’s unknot? (In particular, I presume it was already known to be unknotted?) Presumably Musick has an implementation of his algorithm – is it publicly available?

I don’t yet have a fully computerized implementation of the algorithm. I have a program that will solve many knots (up to about 100 crossing or so), but there are certain valid moves that the program doesn’t yet see. For example, it can’t do Haken’s “Gordian Unknot”, though I have found an unknotting sequence by hand. I’m happy to send the program or sequence to interested researchers, but I’m not ready to post it publicly. At the moment I find the program much more useful for drawing knots than for checking triviality.